Energetic ion distribution resulting from neutral beam injection in tokamaks

The Fokker-Planck equation is studied for an energetic ion beam injected into a magnetized plasma consisting of Maxwellian ions and electrons with υ thi ≪υ b ≪ υ the . The time evolution of the fast ion distribution is given in terms of an infinite sum of Legendre polynomials for distributions that are axisymmetric about the magnetic field. The effect of charge exchange is included. The resulting ion distribution is somewhat isotropic for velocities much less than the injection velocity, however, the distribution is sharply peaked in both energy and pitch angle for velocities near the injection velocity. Approximate asymptotic expressions are given for the distribution in the vicinity of the injected beam and for velocities greater than the injection velocity. The effect of a weak parallel electric field is also given.